Rivera, 43, and six others left Monterrey for Toluca at about 3:30 a.m. Sunday after a concert performance. Air traffic controllers lost contact with the U.S.-registered Learjet 25 about 10 minutes after takeoff.
Mexican authorities found the wreckage from the plane and Rivera's California driver's license at the crash site in Nuevo Leon state, in rugged terrain about 70 miles outside Monterrey. Officials said the impact of the crash was so violent that nothing was recognizable, neither material nor human.
At a press conference outside the Rivera family's Lakewood home Monday, some of Rivera's brother said they were still hopeful that their sister was alive.
"In our eyes, we still have faith that my sister will be OK," said Rivera's brother, Juan. "We have no confirmation of her body being recovered - dead or alive."
Rivera's brother, Lupillo, who is also a a well-known singer, thanked the public for supporting the family through a difficult time.
Other brothers of Rivera said they planned to go to Mexico on Monday to positively identify her remains.
Hector Raphael, Rivera's former tour manager and a longtime family friend, arrived in Monterrey on Monday and said Rivera's family will not be arriving to Mexico until authorities are ready for them to retrieve her remains. He said the family has not been given clear answers.
"The information is just so hard to get," Raphael said. "It's very devastating."
"We're just going to try to bring back whatever we can just so she can be at home, at least with my mom and my father and the rest of the family. We need her here," said Rivera's brother, Gustavo.
The small plane was 43 years old. Records show that it had sustained substantial damage in an accident in 2005 when it experienced a fuel system malfunction. The National Transportation Safety Board has stepped in to help the Mexican government investigate the crash.
Rivera's family said they plan to hold a memorial service so fans will have an opportunity to say goodbye to the singer.
Rivera, a Long Beach native, has sold more than 15 million records. Known as the "Diva of Banda," she was one of the biggest stars in the male-dominated genre. She also had a TV show and appeared in movies. She recently won two Billboard Mexican Music Awards for Female Artist of the Year and Banda Album of the Year. Rivera was slated to star in her own TV show on ABC.
The singer recently divorced Major League Baseball pitcher Esteban Loaiza. She leaves behind five children and two grandchildren.
A vigil was held outside the family's home in Lakewood on Monday evening. They sang her songs in remembrance.